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          <h1 class="post-title" itemprop="name headline">图的遍历:BFS和DFS

            
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              <time title="创建时间：2019-09-03 19:24:07" itemprop="dateCreated datePublished" datetime="2019-09-03T19:24:07+08:00">2019-09-03</time>
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        <h1 id="图的遍历"><a href="#图的遍历" class="headerlink" title="图的遍历"></a>图的遍历</h1><h2 id="BFS（广度优先搜索）"><a href="#BFS（广度优先搜索）" class="headerlink" title="BFS（广度优先搜索）"></a>BFS（广度优先搜索）</h2><h3 id="算法原理及步骤"><a href="#算法原理及步骤" class="headerlink" title="算法原理及步骤"></a>算法原理及步骤</h3><p>按照广度优先原则遍历图，利用了队列，有点像树的层次遍历。广度优先遍历的结果不唯一。整个遍历过程大概是这样的：给定一个起始顶点，将该起始顶点入队</p><ol>
<li>顶点出队，如果当前顶点未被标记访问，则访问该顶点，然后标记为已访问，如果当前顶点已访问则直接丢弃该顶点</li>
<li>当前访问顶点的邻接顶点入队</li>
<li>当队列不为空的时候，循环1,2步</li>
</ol><a id="more"></a>

<h4 id="算法流程"><a href="#算法流程" class="headerlink" title="算法流程"></a>算法流程</h4><div id="flowchart-0" class="flow-chart"></div>

<h4 id="算法实现"><a href="#算法实现" class="headerlink" title="算法实现"></a>算法实现</h4><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 广度优先遍历</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">bfs</span><span class="params">(self, start)</span>:</span></span><br><span class="line">    <span class="keyword">if</span> <span class="keyword">not</span> self._invalid(start):</span><br><span class="line">        <span class="keyword">raise</span> GraphError(<span class="string">"不存在"</span> + start + <span class="string">"这样的顶点"</span>)</span><br><span class="line">    queue = [start]  <span class="comment"># 队列实现BFS</span></span><br><span class="line">    seen = set(start)  <span class="comment"># 记录访问过的顶点</span></span><br><span class="line">    parent = &#123;start: <span class="literal">None</span>&#125;  <span class="comment"># Node代表根节点，数组形式保存树</span></span><br><span class="line">    result = []</span><br><span class="line">    <span class="keyword">while</span> queue.__len__() &gt; <span class="number">0</span>:  <span class="comment"># 队非空时</span></span><br><span class="line">        vertex = queue.pop(<span class="number">0</span>)  <span class="comment"># 队首顶点出队</span></span><br><span class="line">        nodes = self._graph[vertex]  <span class="comment"># 获得其邻接顶点</span></span><br><span class="line">        <span class="keyword">for</span> node <span class="keyword">in</span> nodes:</span><br><span class="line">            <span class="keyword">if</span> node <span class="keyword">not</span> <span class="keyword">in</span> seen:</span><br><span class="line">                queue.append(node)  <span class="comment"># 其邻接顶点如果没有被访问，则入队，并且保留父顶点</span></span><br><span class="line">                seen.add(node)</span><br><span class="line">                parent[node] = vertex</span><br><span class="line">        result.append(vertex)</span><br><span class="line">    <span class="keyword">return</span> result, parent</span><br></pre></td></tr></table></figure>

<h4 id="测试"><a href="#测试" class="headerlink" title="测试"></a>测试</h4><p>例如遍历下图</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190825160305.png!blog" alt="20190825160305"></p>
<p>具体的存储结构为：</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line">data = &#123;</span><br><span class="line">    <span class="string">"A"</span>: &#123;<span class="string">"B"</span>: <span class="number">5</span>, <span class="string">"C"</span>: <span class="number">1</span>&#125;,</span><br><span class="line">    <span class="string">"B"</span>: &#123;<span class="string">"A"</span>: <span class="number">5</span>, <span class="string">"C"</span>: <span class="number">2</span>, <span class="string">"D"</span>: <span class="number">1</span>&#125;,</span><br><span class="line">    <span class="string">"C"</span>: &#123;<span class="string">"A"</span>: <span class="number">1</span>, <span class="string">"B"</span>: <span class="number">2</span>, <span class="string">"D"</span>: <span class="number">4</span>, <span class="string">"E"</span>: <span class="number">8</span>&#125;,</span><br><span class="line">    <span class="string">"D"</span>: &#123;<span class="string">"B"</span>: <span class="number">1</span>, <span class="string">"C"</span>: <span class="number">4</span>, <span class="string">"E"</span>: <span class="number">3</span>, <span class="string">"F"</span>: <span class="number">6</span>&#125;,</span><br><span class="line">    <span class="string">"E"</span>: &#123;<span class="string">"C"</span>: <span class="number">8</span>, <span class="string">"D"</span>: <span class="number">3</span>&#125;,</span><br><span class="line">    <span class="string">"F"</span>: &#123;<span class="string">"D"</span>: <span class="number">6</span>&#125;,</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">test_bfs</span><span class="params">(self)</span>:</span></span><br><span class="line">    print(<span class="string">"bfs测试："</span>)</span><br><span class="line">    bfs, bfsparent = TestGraph.g.bfs(<span class="string">"A"</span>)</span><br><span class="line">    print(<span class="string">"BFS:"</span> + graph.GraphAL.printPath(bfs))</span><br><span class="line">    print(<span class="string">"BFS生成路径:"</span> + bfsparent.__str__())</span><br><span class="line">    print(<span class="string">"BFS生成路径打印："</span> + graph.GraphAL.printTreePath(bfsparent).__str__())</span><br><span class="line">    <span class="keyword">pass</span></span><br></pre></td></tr></table></figure>

<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190829183358.png!blog" alt="20190829183358"></p>
<h3 id="DFS（深度优先搜索）"><a href="#DFS（深度优先搜索）" class="headerlink" title="DFS（深度优先搜索）"></a>DFS（深度优先搜索）</h3><h4 id="算法原理及步骤-1"><a href="#算法原理及步骤-1" class="headerlink" title="算法原理及步骤"></a>算法原理及步骤</h4><p>DFS和BFS很像，不过DFS是深度优先的原则，具体实现是栈。</p>
<p>DFS遍历的结果不唯一。整个遍历过程大概是这样的：给定一个起始顶点，将该起始顶点入栈</p>
<ol>
<li>顶点出栈，如果当前顶点未被标记访问，则访问该顶点，然后标记为已访问，如果当前顶点已访问则直接丢弃该顶点</li>
<li>当前访问顶点的邻接顶点入栈</li>
<li>当栈不为空的时候，循环1,2步</li>
</ol>
<div id="flowchart-1" class="flow-chart"></div>

<h4 id="算法实现-1"><a href="#算法实现-1" class="headerlink" title="算法实现"></a>算法实现</h4><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 深度优先遍历</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">dfs</span><span class="params">(self, start)</span>:</span></span><br><span class="line">    <span class="keyword">if</span> <span class="keyword">not</span> self._invalid(start):</span><br><span class="line">        <span class="keyword">raise</span> GraphError(<span class="string">"不存在"</span> + start + <span class="string">"这样的顶点"</span>)</span><br><span class="line">    stack = [start]  <span class="comment"># 栈实现DFS</span></span><br><span class="line">    seen = set(start)  <span class="comment"># 记录访问过的顶点</span></span><br><span class="line">    parent = &#123;start: <span class="literal">None</span>&#125;  <span class="comment"># Node代表根节点，数组形式保存树</span></span><br><span class="line">    result = []</span><br><span class="line">    <span class="keyword">while</span> stack.__len__() &gt; <span class="number">0</span>:  <span class="comment"># 栈非空时</span></span><br><span class="line">        vertex = stack.pop()  <span class="comment"># 顶点出栈</span></span><br><span class="line">        nodes = self._graph[vertex]  <span class="comment"># 获取出栈顶点的邻接顶点</span></span><br><span class="line">        <span class="keyword">for</span> node <span class="keyword">in</span> nodes:</span><br><span class="line">            <span class="keyword">if</span> node <span class="keyword">not</span> <span class="keyword">in</span> seen:</span><br><span class="line">                stack.append(node)</span><br><span class="line">                seen.add(node)</span><br><span class="line">                parent[node] = vertex</span><br><span class="line">        result.append(vertex)</span><br><span class="line">    <span class="keyword">return</span> result, parent</span><br></pre></td></tr></table></figure>

<h4 id="测试-1"><a href="#测试-1" class="headerlink" title="测试"></a>测试</h4><p>例如遍历下图</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190825160305.png!blog" alt="20190825160305"></p>
<h5 id="存储结构"><a href="#存储结构" class="headerlink" title="存储结构"></a>存储结构</h5><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line">data = &#123;</span><br><span class="line">    <span class="string">"A"</span>: &#123;<span class="string">"B"</span>: <span class="number">5</span>, <span class="string">"C"</span>: <span class="number">1</span>&#125;,</span><br><span class="line">    <span class="string">"B"</span>: &#123;<span class="string">"A"</span>: <span class="number">5</span>, <span class="string">"C"</span>: <span class="number">2</span>, <span class="string">"D"</span>: <span class="number">1</span>&#125;,</span><br><span class="line">    <span class="string">"C"</span>: &#123;<span class="string">"A"</span>: <span class="number">1</span>, <span class="string">"B"</span>: <span class="number">2</span>, <span class="string">"D"</span>: <span class="number">4</span>, <span class="string">"E"</span>: <span class="number">8</span>&#125;,</span><br><span class="line">    <span class="string">"D"</span>: &#123;<span class="string">"B"</span>: <span class="number">1</span>, <span class="string">"C"</span>: <span class="number">4</span>, <span class="string">"E"</span>: <span class="number">3</span>, <span class="string">"F"</span>: <span class="number">6</span>&#125;,</span><br><span class="line">    <span class="string">"E"</span>: &#123;<span class="string">"C"</span>: <span class="number">8</span>, <span class="string">"D"</span>: <span class="number">3</span>&#125;,</span><br><span class="line">    <span class="string">"F"</span>: &#123;<span class="string">"D"</span>: <span class="number">6</span>&#125;,</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h5 id="测试结果"><a href="#测试结果" class="headerlink" title="测试结果"></a>测试结果</h5><p>```python<br>图的结构为：<br>(‘A’, {‘B’: 5, ‘C’: 1})<br>(‘B’, {‘A’: 5, ‘C’: 2, ‘D’: 1})<br>(‘C’, {‘A’: 1, ‘B’: 2, ‘D’: 4, ‘E’: 8})<br>(‘D’, {‘B’: 1, ‘C’: 4, ‘E’: 3, ‘F’: 6})<br>(‘E’, {‘C’: 8, ‘D’: 3})<br>(‘F’, {‘D’: 6})</p>
<p>dfs测试：<br>DFS:A-&gt;C-&gt;E-&gt;D-&gt;F-&gt;B<br>DFS生成路径:{‘A’: None, ‘B’: ‘A’, ‘C’: ‘A’, ‘D’: ‘C’, ‘E’: ‘C’, ‘F’: ‘D’}<br>DFS生成路径打印：<br>A-&gt;B<br>A-&gt;C<br>A-&gt;C-&gt;D<br>A-&gt;C-&gt;E<br>A-&gt;C-&gt;D-&gt;F<br>```<script src="https://cdnjs.cloudflare.com/ajax/libs/raphael/2.2.7/raphael.min.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/flowchart/1.6.5/flowchart.min.js"></script><textarea id="flowchart-0-code" style="display: none">st=>start: 初始化队列，初始顶点入队
e=>end: 结束BFS
deque=>operation: 出队
isVisit=>condition: 是否访问过该顶点?
visit=>inputoutput: 访问
jump=>operation: 跳过该顶点的访问
isqueNull=>condition: 是否队空

st->deque->isVisit
isVisit(yes)->jump->isqueNull
isVisit(no)->visit->isqueNull
isqueNull(yes)->e
isqueNull(no)->deque</textarea><textarea id="flowchart-0-options" style="display: none">{"scale":1,"line-width":2,"line-length":50,"text-margin":10,"font-size":12}</textarea><script>  var code = document.getElementById("flowchart-0-code").value;  var options = JSON.parse(decodeURIComponent(document.getElementById("flowchart-0-options").value));  var diagram = flowchart.parse(code);  diagram.drawSVG("flowchart-0", options);</script><textarea id="flowchart-1-code" style="display: none">st=>start: 初始化栈，初始顶点进栈
e=>end: 结束DFS
deque=>operation: 出栈
isVisit=>condition: 是否访问过该顶点?
visit=>inputoutput: 访问
jump=>operation: 跳过该顶点的访问
isqueNull=>condition: 是否栈空

st->deque->isVisit
isVisit(yes)->jump->isqueNull
isVisit(no)->visit->isqueNull
isqueNull(yes)->e
isqueNull(no)->deque</textarea><textarea id="flowchart-1-options" style="display: none">{"scale":1,"line-width":2,"line-length":50,"text-margin":10,"font-size":12}</textarea><script>  var code = document.getElementById("flowchart-1-code").value;  var options = JSON.parse(decodeURIComponent(document.getElementById("flowchart-1-options").value));  var diagram = flowchart.parse(code);  diagram.drawSVG("flowchart-1", options);</script></p>

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